Consider parallel lines cut by a transversal.
Parallel lines q and s are cut by transversal r. On line q where it intersects line r, 4 angles are created. Labeled clockwise, from uppercase left: angle 1, angle 2, angle 4, angle 3. On line s where it intersects line r, 4 angles are created. Labeled clockwise, from uppercase left: angle 5, angle 6, angle 8, angle 7.
Explain which theorems, definitions, or combinations of both can be used to prove that alternate exterior angles are congruent.
Answers
When two parallel lines are cut by a transverse. the angles formed on the exterior of the parallel lines, on the opposite sides of the transverse are known as the Alternate Exterior Angle.
What are Alternate exterior angles?When two parallel lines are cut by a transverse. the angles formed on the exterior of the parallel lines, on the opposite sides of the transverse are known as the Alternate Exterior Angle.
Firstly, ∠1 and ∠7 are alternate exterior angles as shown in the image, now to prove if these two angles will be congruent we can use the below proof.
First Method:
∠1 + ∠2 = 180° {Supplementary angles because both lies on the line q}
∠2 = (180° - ∠1)
Similarly, ∠2 = ∠6 = (180° - ∠1), corresponding angles are equal,
∠6 + ∠7 = 180° {Supplementary angles because both lies on the line r}
∠7 = 180° - ∠6
∠7 = 180° - (180° - ∠1)
∠7 = 180° - 180° + ∠1
∠7 = ∠1
OR
Second Method:
∠1 = ∠3 {Vertical angles formed by intersecting lines q and r}
∠3 = ∠5 {Alternate Interior angles}
∠5 = ∠7 {Vertical angles formed by intersecting lines s and r}
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Related Questions
PLEASE HELP MULTIPLE CHOICE (photo of question attached) WILL GIVE BRAINLEIST!
The triangles on the grid below represent a translation.
To form the image, the pre-image moved
a. five units right and three units up.
b. two units right and three units up.
c. five units left and three units down.
d. two units left and three units down.
Answers
Answer:
A five units right and three units up
Step-by-step explanation:
take coordinate C for example and count how many spaces you need to go either right or left and then up and down for the two triangles to be in the same place
A. The two spinners shown below are being used in a probability experiment.
During each trial of the experiment, the arrows on the spinners are spun once, and the outcome is recorded. For example, an outcome of (2, 1) means that the arrow pointed to 2 on the first spinner and pointed to 1 on the second spinner.
B. What is the theoretical probability that, during each trial of the experiment, the result has at least one 4 on the spinners? Show your work or explain your answer.
Explain why the experimental probability from the results does not agree with the theoretical probability you found in part B.
Answers
The theoretical probability of at least one 4 on the spinners is 0.4375
(a) The number of different outcomesThe sections on the spinners are:
Spinner 1 = 4
Spinner 2 = 4
So, the number of different outcomes is:
Outcomes = 4 * 4
Outcomes = 16
Hence, the number of different outcomes is 16
(b) The theoretical probability of at least one 4 on the spinnersThe spin results that have at least one 4 are:
Results = {(4,1), (4,2), (4,3), (4,4), (1,4), (2,4), (3,4)}
The count of these results is 7.
So, the theoretical probability of at least one 4 on the spinners is:
P = 7/16
P = 0.4375
Hence, the theoretical probability of at least one 4 on the spinners is 0.4375
(c) Why the theoretical probability and the experimental probability are different?The theoretical probability and the experimental probability are different because:
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Find the area of a regular octagon with an apothem of 2 cm.
Answers
The area of a regular octagon with an apothem of 2 cm is 3cm ^2.
The area of a regular octagon with an apothem of 2 cm.
Given the apothem length,
What is the area of the regular polygon?the area of a regular polygon becomes,
[tex]A=\frac{1}{2}\times P\times A[/tex]
P= the perimeter of the regular polygon
A is the apothem of the regular polygon
Here, we get
p=2=2cm, a=3cm.
So, plugging in the given values, we get
[tex]A=\frac{1}{2} \times 2cm\times 3cm[/tex]
A=1cm⋅3cm
A=3cm^2
Therefore the area of a regular octagon with an apothem of 2 cm is 3cm ^2.
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What other areas of human or societal change have models that would fit an
exponential curve?
Answers
[tex]\large\bold{\underline{\underline{Answer:-}}}[/tex]
There are smooth exponential curves that control price performance, capacity, and bandwidth so it easy to predict the cost of something in the future. He said, "When people think about the future they think about it lineraly.
Given that the expression “p dollars for every q items” describes a unit price, which statement must be true?
Answers
The complete question is
"Given that the expression “p dollars for every q items” describes a unit price, which statement must be true?
p = 1
p = q
q = 1
pq = 1"
The statement that must be true would be from option D; pq = 1.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that the expression “p dollars for every q item” describes a unit price,
So, the equation will be formed as
p x q = 1
pq = 1
Hence, the statement that must be true would be from option D; pq = 1.
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ab (2a²b² - 4b) = what is the answer
Answers
Image below is simplified answer!
Answer:
2ab(a2b−2)
Step-by-step explanation:
What is the area of a sector with measure of arc equal to 90° and radius equal to 1 foot?
Answers
Answer:
0.7855 square feet
Step-by-step explanation:
90/360×3.142×1 squared
=0.7855
Examine the system of equations.
y=2x-3
y=-3
Which statement about the system of linear equations
is true?
O The lines have different slopes.
O There is no solution to the system.
O The lines have the same slope, but different y-
intercepts.
O The solution is (-3, -9).
Answers
For a system of equations to have no real solution, the lines of the equations must be parallel to each other. The correct option is A.
What is the System of equations?Inconsistent System
For a system of equations to have no real solution, the lines of the equations must be parallel to each other.
Consistent System
1. Dependent Consistent System
For a system of the equation to be a Dependent Consistent System, the system must have multiple solutions for which the lines of the equation must be coinciding.
2. Independent Consistent System
For a system of the equation to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.
If the two of the given system of equations are plotted on the graph, then it can be observed that the two lines have different slopes. Therefore, the correct option is A.
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help with both please :)
Answers
Answer: I know two methods of solving both of the sums. One is the method of elimination, the other is method of substitution. You can do any of the given methods which is easier for you. Both methods will be shown below:
Method of Elimination1) 5x + y = 9 - - - - (i)
10x - 7y = - 18 - - - - (ii)
eq. (i) multiplied by 2
10x + 2y = 18 - - - - (i)
10x - 7y = - 18 - - - - (ii) {subtraction of eq. (ii) from eq. (i)}
0 + 9y = 36
y = 36/9
y = 4
From eq. (i),
5x + y = 9
-> 5x + 4 = 9
-> 5x = 9 - 4
-> x = 5/5
-> x = 1
So, x = 1 and y = 4
2) - 4x + 9y = 9 - - - - (i)
x - 3y = - 6 - - - - (ii)
eq. (ii) multiplied by 3
- 4x + 9y = 9 - - - - (i)
3x - 9y = - 18 - - (ii) {addition of eq. (ii) and eq. (i)}
- x + 0 = - 9
x = 9
From eq. (ii),
x - 3y = - 6
-> 9 - 3y = - 6
-> - 3y = -6-9
-> y = -15/-3
-> y = 5
So, x = 9 and y = 5
Method of Substitution1) 5x + y = 9 - - - - (i)
10x - 7y = - 18 - - - - (ii)
eq. (i)
5x + y = 9
-> y = 9 - 5x
Value of eq. (i) in eq. (ii)
10x - 7y = - 18
-> 10x - 7(9 - 5x) = - 18
-> 10x - 63 + 35x = - 18
-> 45x = - 18 + 63
-> x = 45/45
-> x = 1
From eq. (i),
5x + y = 9
-> 5 + y = 9
-> y = 9 - 5
-> y = 4
So, x = 1 and y = 4
2) - 4x + 9y = 9 - - - - (i)
x - 3y = - 6 - - - - (ii)
eq. (i)
- 4x + 9y = 9
-> - 4x = 9 - 9y
-> x = (9 - 9y) / -4
Value of eq. (i) in eq. (ii)
x - 3y = - 6
-> (9 - 9y) / -4 -3y = - 6
-> (9 - 9y + 12y) = - 6 * - 4
-> 3y = 24 - 9
-> y = 15/3
-> y = 5
From eq. (ii)
x - 3y = - 6
-> x - 3(5) = - 6
-> x - 15 = - 6
-> x = - 6 + 15
-> x = 9
So, x = 9 and y = 5
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Select the correct answer.
The speed of a ship is given by , where d is the distance the ship travels in 3 hours. If the ship travels 48 miles in 3 hours, what is the speed of the ship?
A.
12 miles per hour
B.
16 miles per hour
C.
45 miles per hour
D.
51 miles per hour
Answers
What value of a make the equation 14-a=19-12
Answers
[tex]14-a=19-12\\14-a=7\\a=14-7\\a=7[/tex]
Answer:
7
Step-by-step explanation:
14-a=19-12
14-a=7
14-7=a
7=a
Combine like terms
Given the sequence in the table, which of the following represents the sum for term 5 through term 11 in sigma notation? (1 point)
a an
1 2
2 −10
3 50
Answers
Answer:
Given sequence in the table is a Geometric sequence and The sum for term 5 through term 11 in sigma notation is given by:
[tex]$\sum_{n=5} ^{\111} 2(-5)^n^-^1$[/tex]
Step-by-step explanation:
Geometric sequence - it is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio
here the given terms :
a1 = 2, a2 = -10, a3 = 50
you can see it is a geometric sequence as the ratio is constant [tex]\frac{a2}{a1}{=}\frac{a3}{a2}{=}{-5}[/tex]
now the nth term for geometric sequence :
[tex]a_{n} {=}{a}{r}^{n-1}[/tex]
here,
a = first term.r = common ratio of the given terms.n = number of terms in geometric sequence.now substituting the given values in the expression,
[tex]a_{n} {=}{2}{{(}-5}{)}^{n-1}[/tex]
we have to find the sum from term 5 to term 11,
therefore using sigma notation and putting n= 5 and n=11 at the below and above the sigma respectively,
[tex]$\sum_{n=5} ^{\111} 2(-5)^n^-^1$[/tex]
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Solve the following...
6x - 5 = -9x -9
Answers
Answer:
6x - 5 = (-9x) - 9
6x + 9x = (-9) + 5
15x = (-4)
x = (-4/15)
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:x = -\cfrac{4}{15} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: 6x - 5 = - 9x - 9[/tex]
[ add 9x and 5 on both sides ]
[tex]\qquad \tt \rightarrow \: 6x - 5 + 9x + 5 = - 9x - 9 + 9x + 5[/tex]
[tex]\qquad \tt \rightarrow \: 6x + 9x = - 9 + 5[/tex]
[tex]\qquad \tt \rightarrow \: 15x = - 4[/tex]
[tex]\qquad \tt \rightarrow \: x = - \cfrac{4}{15} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Simplify this radical.
[tex]\sqrt{84} \\\\1; 2\sqrt{21} \\2; 2\sqrt{42} \\3; 4\sqrt{21} \\or 4; 4\sqrt{42} \\[/tex]
Answers
The radical is 2√21.
What is radical?The √ symbol that is used to denote square root or nth roots.
Given :
√84
= √2*2*21
=2√21
Hence, the radical is 2√21.
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Sienna is solving the quadratic equation by completing the square.
3x2 + 9x – 4 = 0
3x2 + 9x = 4
A(x2 + 3x) = 4
Answers
Answer:
See below
Step-by-step explanation:
3 (x^2 + 3x) = 4
3 ( x + 3/2)^2 = 4 + 27/4
Figure B is a scaled copy of figure A.
What is the scale factor from figure A to figure B
Answers
Answer:
1/3
Step-by-step explanation:
We multiply 33(Figure A side) by 1 /3 to get 11(Figure B side).
enlist any five common social rules all kinds of society
Answers
Answer:Shake hands when you meet someone.Make direct eye contact with the person you are speaking with.Unless the movie theater is crowded, do not sit right next to someone.Do not stand close enough to a stranger to touch arms or hips.Cover your coughs.
Step-by-step explanation:trust me
Figure 1 is similar to figure 2. What is TS?
1 unit
4 units
8 units
2 units
Answers
Answer:
8 units
Step-by-step explanation:
ratios
(x-3) /( x+1) = (x-2)/(x+3) cross multiply
x^2 -x -2 = x^2 - 9
-x - 2 + 9 = 0
x = 7
so TS = x + 1 = 8 units
Which equation can replace 3x + 5y = 59 in the original system and still produce the same solution?
Answers
Answer:
13x = 39
x=3
y=10
What is the solution for the system of x - y = -1 and 2x - 5y = -5 ?
Show your work.
Answers
Step-by-step explanation:
please mark me as brainlest
x - y = -1 multiply by 5
we get 5x -5y = -5
subtract the equations:
5x - 5y = -5
-
2x - 5y = -5
5x - 5y -(2x - 5y ) = - 5 - - 5
5x - 5y - 2x + 5y =0
3x = 0
x = 0
2(0) - 5y = -5
- 5y = -5
y = 1
is 8.6 a rational number
Answers
Answer:
Yes
Step-by-step explanation:
Yes, 8.6 is a rational number because it can be expressed in the form of p/q
[tex]8.6 = \frac{86}{10} = \frac{43}{5} [/tex]
find the least nu,ber which is exactly divisible by 12 16 and 24
Answers
Answer:
The smallest number all three numbers can be divided by is 4.
Step-by-step explanation:
12/4=3
16/4=4
24/4=6
Hope this helps!
If not, I am sorry.
Select the correct answer.
Which value of x makes this equation true?
-12x2(x + 9) = 5(x + 4)
O A.
OB.
O C.
O D.
Answers
Answer:
B. -2
Step-by-step explanation:
-12x -2(x+9) = 5(x+4)
*ALWAYS REMEMBER YOUR BODMAS*
-12x -2x - 18 = 5x + 20
*group the like terms*
-14x - 5x = 20 + 18
-19x = 38
x = -2
The value of x that makes the equation true is: x = -2.
B. -2.
Here, we have to find the value of x that makes the equation true, we need to solve for x.
Let's solve the equation step by step:
-12x - 2(x + 9) = 5(x + 4)
Distribute the -2 and 5 on the right side of the equation:
-12x - 2x - 18 = 5x + 20
Combine like terms on both sides:
-14x - 18 = 5x + 20
Move the variable terms (5x) to one side of the equation and the constant terms to the other side.
Let's subtract 5x from both sides:
-14x - 5x - 18 = 5x - 5x + 20
-19x - 18 = 20
Move the constant term (-18) to the other side of the equation.
Let's add 18 to both sides:
-19x - 18 + 18 = 20 + 18
-19x = 38
Finally, divide both sides by -19 to isolate x:
x = 38 / -19
x = -2
So, the value of x that makes the equation true is: x = -2.
B. -2.
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What is the scale factor of this dilation?
Answers:
A. 1/2
B.3/5
C.1 2/3
D.2
Answers
Answer:
3/5
Step-by-step explanation:
scale factor of ab to A'B'
AB:A'B'
5 : 3
in fraction the scale
factor is 3
—
5
heance a reduction.
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To support a shelf, the diameter of a bolt can measure anywhere from 0.2 cm less than 1.5 cm to 0.2 cm greater than 1.5 cm. Which graph represents the possible measures of the diameter of the bolt?
Answers
please help me i need help quick
Answers
Answer:
x = -2
y = -6
Step-by-step explanation:
Equating the equations :
x - 4 = 4x + 23x = -6x = -2y = -2 - 4y = -6Equate both
x-4=4x+2-4-2=4x-x-6=3xx=-2And
y=-2-4=-6Graph attached
If side c measures 32.3 units long, how long is side a?
Answers
Answer:
16.15
Step-by-step explanation:
sin(30) = a / c
a = c * sin(30)
a = 32.3 * 0.5
a = 16.15
Find the LinReg line of best fit for this data set.
{(−5, 6.3), (−4, 5.6), (−3, 4.8), (−2, 3.1), (−1, 2.5), (0, 1.0), (1, −1.4)}
Answers
The LinReg line of best fit for this data set is ŷ = -1.24X + 0.66
What is regression line?A linear regression line has an equation of the form Y = a + bX, where X is the explanatory variable and Y is the dependent variable.
Given:
(−5, 6.3),
(−4, 5.6),
(−3, 4.8),
(−2, 3.1),
(−1, 2.5),
(0, 1.0),
(1, −1.4)
Sum of X = -14
Sum of Y = 21.9
Mean X = -2
Mean Y = 3.1286
Sum of squares (SSX) = 28
Sum of products (SP) = -34.6
Regression Equation,
ŷ = bX + a
b = SP/SSX = -34.6/28 = -1.23571
a = MY - bMX = 3.13 - (-1.24*-2) = 0.65714
ŷ = -1.23571X + 0.65714
ŷ = -1.24X + 0.66
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Joanne has a pile of nickels and a pile of dimes. She counts her money and discovers that she has 30 nickels and 10 dimes. Let x represent the number of nickels and y represent the number of dimes. (HINT: Use the values of the coins.) How much money does Joanne have in total?
Total Amount: $_____
Answers
$2.50
Step-by-step explanation:
10 dimes are 100 aka 1 dollar, and 30 nickels make 250
Solve the equation for x.
√x-5 = x-11
Answers
Answer:
√x-5 = x-11 = 9.
Step-by-step explanation:
Isolate the radical, then raise each side of the equation to the power of its index.
x = 9 Solve the equation for x.